Ahmad, Archie and Lee started walking at the same time from the same starting point round a circular track. Lee walked in the clockwise direction. Ahmad and Archie walked in an anti-clockwise direction. Lee took 5 min to complete each round. He met Ahmad after every 3 minutes. He met Archie after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Lee complete in 1 h?
2. When Lee and Ahmad met again at the starting point after 1 h, Archie had completed 1.2 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

Number of rounds that Lee completed in 1 h
= 60 ÷ 5
= 12

(b)
Lee took 5 min to complete 1 round
1 min = ¹₅ of circular track = 1 u
5 min = ⁵₅ of circular track = 5 u

Lee's distance is the repeated identity.
Make Lee's distance the same.

Lee's distance : Ahmad's distance
3 : 5 - 3
3 : 2

Lee's distance : Archie's distance
4 : 5 - 4
4 : 1

Lee	Ahmad	Archie
3x4	2x4
4x3		1x3
12	8	3

The distance of Lee is the repeated identity. 
LCM of 3 and 4 = 12

In 1 h
Lee's rounds : Ahmad's rounds : Archie's rounds
12 : 8 : 3

Distance that Archie completed in 1 h = 1.2 km

3 rounds = 1.2 km = 1200 m

1 round = 1200 ÷ 3 = 400 m

Circumference of the circular track = 400 m

Answer(s): (a) 12; (b) 400 m